(13+2x)(8+2x)=153

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Solution for (13+2x)(8+2x)=153 equation: 


Simplifying
(13 + 2x)(8 + 2x) = 153

Multiply (13 + 2x) * (8 + 2x)
(13(8 + 2x) + 2x * (8 + 2x)) = 153
((8 * 13 + 2x * 13) + 2x * (8 + 2x)) = 153
((104 + 26x) + 2x * (8 + 2x)) = 153
(104 + 26x + (8 * 2x + 2x * 2x)) = 153
(104 + 26x + (16x + 4x2)) = 153

Combine like terms: 26x + 16x = 42x
(104 + 42x + 4x2) = 153

Solving
104 + 42x + 4x2 = 153

Solving for variable 'x'.

Reorder the terms:
104 + -153 + 42x + 4x2 = 153 + -153

Combine like terms: 104 + -153 = -49
-49 + 42x + 4x2 = 153 + -153

Combine like terms: 153 + -153 = 0
-49 + 42x + 4x2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-12.25 + 10.5x + x2 = 0

Move the constant term to the right:

Add '12.25' to each side of the equation.
-12.25 + 10.5x + 12.25 + x2 = 0 + 12.25

Reorder the terms:
-12.25 + 12.25 + 10.5x + x2 = 0 + 12.25

Combine like terms: -12.25 + 12.25 = 0.00
0.00 + 10.5x + x2 = 0 + 12.25
10.5x + x2 = 0 + 12.25

Combine like terms: 0 + 12.25 = 12.25
10.5x + x2 = 12.25

The x term is 10.5x.  Take half its coefficient (5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
10.5x + 27.5625 + x2 = 12.25 + 27.5625

Reorder the terms:
27.5625 + 10.5x + x2 = 12.25 + 27.5625

Combine like terms: 12.25 + 27.5625 = 39.8125
27.5625 + 10.5x + x2 = 39.8125

Factor a perfect square on the left side:
(x + 5.25)(x + 5.25) = 39.8125

Calculate the square root of the right side: 6.309714732

Break this problem into two subproblems by setting 
(x + 5.25) equal to 6.309714732 and -6.309714732.


Subproblem 1
x + 5.25 = 6.309714732

Simplifying
x + 5.25 = 6.309714732

Reorder the terms:
5.25 + x = 6.309714732

Solving
5.25 + x = 6.309714732

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5.25' to each side of the equation.
5.25 + -5.25 + x = 6.309714732 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + x = 6.309714732 + -5.25
x = 6.309714732 + -5.25

Combine like terms: 6.309714732 + -5.25 = 1.059714732
x = 1.059714732

Simplifying
x = 1.059714732


Subproblem 2
x + 5.25 = -6.309714732

Simplifying
x + 5.25 = -6.309714732

Reorder the terms:
5.25 + x = -6.309714732

Solving
5.25 + x = -6.309714732

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-5.25' to each side of the equation.
5.25 + -5.25 + x = -6.309714732 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + x = -6.309714732 + -5.25
x = -6.309714732 + -5.25

Combine like terms: -6.309714732 + -5.25 = -11.559714732
x = -11.559714732

Simplifying
x = -11.559714732


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.059714732, -11.559714732}

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